Two-soliton solutions of the complex short pulse equation via Riemann–Hilbert approach

Zhang, Weiguo; Ye, Qian; Bo, Ge-Qiang

doi:10.1016/j.aml.2019.06.023

Cited by 7 publications

(5 citation statements)

References 4 publications

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“…With the in-depth study of nonlinear systems, there have been many mature methods to study the important properties of nonlinear systems. such as Darboux transformation [1,2], Hirota bilinear method [3][4][5], Bäcklund transformation [6,7], Riemann-Hilbert method [8][9][10][11][12][13], Painlevé analysis [14,15] and algebra-geometric method [16,17]. These methods have made great contributions to the study of nonlinear system solutions, integrability, symmetry, scattering problems and long time asymptotic behavior, etc.…”

Section: Introductionmentioning

confidence: 99%

The Dbar-dressing method for the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation

Sun,

2024

Commun. Theor. Phys.

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In this work, the (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation is studied by means of Dbar-dressing method. A new Dbar problem has been constructed by analyzing the characteristic function and the Green's function of its Lax representation. Based on solving the Dbar equation and choosing the proper spectral transformation, the solution of DJKM equation is constructed. Furthermore, the more general solution of DJKM equation can be also obtained by ensuring the evolution of the time spectral data.

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Section: Introductionmentioning

confidence: 99%

The Dbar-dressing method for the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation

Sun,

2024

Commun. Theor. Phys.

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“…These solutions can further help to understand natural phenomena and laws. In recent years, more and more mathematical physicists have begun to pay attention to Riemann-Hilbert (RH) approach [9,10], which is a new powerful method for solving integrable linear and nonlinear evolution equations [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. The main idea of this method is to establish a corresponding matrix RH problem on the Lax pair of integrable equations.…”

Section: Introductionmentioning

confidence: 99%

Dynamic behaviors of soliton solutions for a three-coupled Lakshmanan–Porsezian–Daniel model

Lin

Zhang

2022

Nonlinear Dyn

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In this paper, we use the Riemann-Hilbert (RH) approach to examine the integrable three-coupled Lakshmanan-Porsezian-Daniel (LPD) model, which describe the dynamics of alpha helical protein with the interspine coupling at the fourth-order dispersion term. Through the spectral analysis of Lax pair, we construct the higher order matrix RH problem for the three-coupled LPD model, when the jump matrix of this particular RH problem is a 4 × 4 unit matrix, the exact N-soliton solutions of the three-coupled LPD model can be exhibited. As special examples, we also investigate the nonlinear dynamical behaviors of the single-soliton, two-soliton, three-soliton and breather soliton solutions. Finally, an integrable generalized N-component LPD model with its linear spectral problem is discussed.

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“…Chen-Lee-Liu derivative nonlinear Schrödinger equation (CLL-NLS equation) was firstly put forward by Kundu [5] which is a completely integrable model, and it can be derived from the modified NLS equation which ignores the mean flow term in hydrodynamics [6]. In recent years, many excellent methods have been put forward by the deep study in integrable system, such as Darboux transformation [7,8], Hirota bilinear method [9][10][11], similarity reduction [12], Riemann-Hilbert approach [13][14][15][16][17] and inverse scattering method [18,19]. Among these but not limited to these methods, Zhang et al obtained higher-order solutions of Eq.…”

Section: Introductionmentioning

confidence: 99%

A $$\overline{\partial }$$-dressing method for the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation

Sun

2022

J Nonlinear Math Phys

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In this work, we apply the $$\overline{\partial }$$ ∂ ¯ -dressing method to study the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation (CLL–NLS) with non-normalization boundary conditions. The spatial and time spectral problems associate with CLL–NLS equation which are derived from local $$2 \times 2$$ 2 × 2 matrix. A CLL–NLS hierachy with source is proposed by using recursive operator. Based on the $$\overline{\partial }$$ ∂ ¯ -equation, the N-solitons of the CLL–NLS equation are constructed by choosing a special spectral transformation matrix. Further more, the explicit two-soliton is obtained.

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Two-soliton solutions of the complex short pulse equation via Riemann–Hilbert approach

Cited by 7 publications

References 4 publications

The Dbar-dressing method for the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation

The Dbar-dressing method for the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation

Dynamic behaviors of soliton solutions for a three-coupled Lakshmanan–Porsezian–Daniel model

A $$\overline{\partial }$$-dressing method for the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation

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